Results 1 to 9 of 9

Math Help - Solving Trig functions?

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    24

    Solving Trig functions?

    I'm not sure how to solve these trig functions;

    1. 2sin(theta)−sqrt(2)tan(theta)= 0 ; 0 ≤ theta < 2pi

    2. sin(theta)cos(theta)−sin(theta)−cos(theta)+1=0 ; 0 ≤ theta < 2pi
    for #2 i factored out the sin(theta) (cos(theta)-1)- cos(theta)+1 =0
    then moved the - cos(theta)+1 to the right side and solved for sin(theta)
    is that right so far? D:
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    1. Multiply through by ]\cos(\theta) and solve by factoring
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,939
    Thanks
    338
    Awards
    1
    Quote Originally Posted by dondonlouie View Post
    2. sin(theta)cos(theta)−sin(theta)−cos(theta)+1=0 ; 0 ≤ theta < 2pi
    for #2 i factored out the sin(theta) (cos(theta)-1)- cos(theta)+1 =0
    then moved the - cos(theta)+1 to the right side and solved for sin(theta)
    is that right so far? D:
    It's probably better to rewrite that first line as
    sin(\theta) \cdot (cos(\theta) - 1) - (cos(\theta) - 1) = 0

    Can you see where to go from here?

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2011
    Posts
    24
    Quote Originally Posted by topsquark View Post
    It's probably better to rewrite that first line as
    sin(\theta) \cdot (cos(\theta) - 1) - (cos(\theta) - 1) = 0

    Can you see where to go from here?

    -Dan
    wouldn't the cos(theta)-1 cancel out leaving sin(theta)=0?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,939
    Thanks
    338
    Awards
    1
    Quote Originally Posted by dondonlouie View Post
    wouldn't the cos(theta)-1 cancel out leaving sin(theta)=0?
    Careful! When you have the equation ab = 0 then either a = 0 or b = 0. So what this equation is saying:
    (sin(\theta) - 1)(cos(\theta) - 1) = 0 \implies sin(\theta) - 1 = 0 \text{ or } cos(\theta) - 1 = 0

    -Dan
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Feb 2011
    Posts
    24
    Quote Originally Posted by topsquark View Post
    Careful! When you have the equation ab = 0 then either a = 0 or b = 0. So what this equation is saying:
    (sin(\theta) - 1)(cos(\theta) - 1) = 0 \implies sin(\theta) - 1 = 0 \text{ or } cos(\theta) - 1 = 0

    -Dan
    how did you get from sin(theta)(cos(theta)-1)-(cos(theta)-1)= 0
    to (sin(theta)-1)(cos(theta)-1)?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,564
    Thanks
    1425
    Take out \displaystyle (\cos{\theta} - 1) as a factor...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Feb 2011
    Posts
    24
    Quote Originally Posted by Prove It View Post
    Take out \displaystyle (\cos{\theta} - 1) as a factor...
    ohhh okay i see it
    thank you so much for helping me
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,939
    Thanks
    338
    Awards
    1
    Quote Originally Posted by dondonlouie View Post
    ohhh okay i see it
    My apologies. I thought you already had factored that.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving trig functions...
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: April 30th 2010, 04:49 AM
  2. Solving trig functions...
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 29th 2010, 11:04 PM
  3. Solving x with Trig Functions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 4th 2010, 05:49 AM
  4. Solving an Integral of Trig Functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 29th 2009, 04:58 PM
  5. Solving Trig Functions?
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: November 9th 2008, 07:16 AM

Search Tags


/mathhelpforum @mathhelpforum